Apparatus for examining a body, particularly useful in tomography, for producing transverse sectional images of the body, comprises scanning means supported by a carriage coupled to its mounting via a pair of links defining, with the carriage and its mounting, a four-link, parallel-motion mechanism which, upon oscillation of the links, effects a curvilinear movement of the carriage with respect to the body, and thereby a curvilinear traverse of the body by the scanning means. The carriage is also rotatably mounted on the machine frame enabling the carriage, and the scanning means supported thereon, also to be rotated about the body either incrementally or continuously.